This phase I/II trial studies the side effects and best dose of genetically engineered lymphocyte therapy and to see how well it works after peripheral blood stem cell transplant (PBSCT) in treating patients with high-risk, intermediate-grade, B-cell non-Hodgkin lymphoma (NHL). Genetically engineered lymphocyte therapy may stimulate the immune system in different ways and stop cancer cells from growing. Giving rituximab together with chemotherapy before a PBSCT stops the growth of cancer cells by stopping them from dividing or killing them. Giving colony-stimulating factors, such as filgrastim (G-CSF), or plerixafor helps stem cells move from the bone marrow to the blood so they can be collected and stored. More chemotherapy or radiation therapy is given to prepare the bone marrow for the stem cell transplant. The stem cells are then returned to the patient to replace the blood-forming cells that were destroyed by the chemotherapy. Giving genetically engineered lymphocyte therapy after PBSCT may be an effective treatment for NHL